Cube3D 立方体数理Maths · Primary school / Middle school
Why do the angles of a triangle add to 180°?
Stretch a triangle sideways and one corner may grow while another shrinks. The sum stays at 180°. Start by arranging copies of the three corners. Then use a parallel line to see why the copies fit for every triangle on a flat plane.
Build a straight angle one piece at a time
Choose Right. The readings are ∠A = 45°, ∠B = 90°, and ∠C = 45°. Add ∠A, then ∠B. The two pieces fill 135°, so predict the size of the gap before adding ∠C. Its final edge lands on the straight guide.
Leave all three pieces in place and choose Obtuse. Drag one vertex or focus it and press an arrow key. The boundaries between the coloured pieces move, but the last edge still meets the guide. Each copy may turn and move; its opening stays equal to its original angle.
Draw the parallel line that explains the result
In triangle ABC draw a line through A parallel to BC. Along that line, on the side facing the triangle, the rays AB and AC divide a straight angle into three smaller angles. The centre angle is ∠A.
AB cuts both parallel lines. Its alternate interior angles are equal, so the adjacent angle on the B side equals ∠B. The same argument with AC gives ∠C on the other side. In this proof the order is ∠B, ∠A, ∠C; the pieces in the lab are in alphabetical order. Changing the order does not change the total of 180°.
Check your understanding
A triangle has angles of 28° and 117°. Find the remaining angle and predict whether the triangle is acute, right or obtuse.
Show the explanation
The remaining angle is 180° − 28° − 117° = 35°. The 117° angle makes the triangle obtuse.
What the model assumes
The experiment uses ordinary flat geometry. It keeps vertices far enough apart to move them and prevents them from collapsing onto a line. The total is calculated from the unrounded interior angles. The experiment requires Family Plus or Teacher access; this note is public.